# If the difference between the roots of the equation is 2 write the values of a.

given x2 + ax + 8 = 0 and α – β = 2

Also from given equation α β = 8

As α – β = 2

Then

α2 - 2 α – 8 =0

(α-4) (α + 2)=0

α = 4 and α = -2

if α = 4 then substituting it in α – β = 2 we get ,

β = 2

from the given equation,

sum of roots = -a

α + β = - a

- a = 4+2

a = -6

if α = - 2 then substituting it in α – β = 2 we get ,

β = - 4

then sum of roots α + β = - a

a = 6

therefore a = ± 6.

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